[Math] double summation notation

Question

In a paper I am studying, the author writes
$$\sum_{{i=1}\atop {k=1}}^{N+1} C_i \eta_k$$
How are the two indices to be interpreted? In other words, how would this expression be written using sigma notation with only one index per sigma?

Answer 1

$$ \sum_{{i=1}\atop {k=1}}^{N+1} C_i \eta_k=\sum_{i=1}^{N+1}\sum_{k=1}^{N+1}C_i \eta_k=\left( \sum_{i=1}^{N+1}C_i \right) \left( \sum_{k=1}^{N+1} \eta_k \right). $$